Neutron Number Dependence of Interference in Two-Neutron Transfer Reactions and the Nuclear Deformation

Abstract

By making use of a simple model for the nuclear deformation, the number dependence of the form factors for inelastic scattering and two-neutron transfer processes are discussed for even-even deformed nuclei in the rare earth region. The form factor amplitudes are expressed in terms of the Legendre polynomials, whose argument is a func­ tion of the number. It is easy to understand, in the perturbative sense, a number dependence of the interference between the direct and two-step processes observed in (p, t) reactions leading to the 0, + and 2, + states. The interference for the 2, + state in deformed nuclei shows a striking parallelism with that for the quadrupole vibrational state in spherical nuclei. It has been shown that the two-neutron transfer reactions on deformed nuclei 1l can be well described in terms of the coupled-channel Born approximation (CCBA), 2l which includes the effect of multi-step processes via inelastic scattering. It has also been dezywnstrated that the same is ;true in the case of the two-neutron transfer reactions leading to the collective vibrational state in spherical nuclei. 3l~sl The purpose of the present paper is to explain,. in the perturbative sense, the neutron number dependence of the interference between direct and two-step processes in the (p, t) and ( t, p) reactions leading to the ground band members in even-even deformed nuclei in the rare earth region. The explanation applies equally well to other deformed nuclei. The interference observed in the (p, t) reactions, leading to the 2 1 + state in the spherical vibrational nuclei has been treated by Udagawa and coworkers. 3l· 5l· 6l They have pointed.ouel.al in the frame­ work of the quasiparticle RPA that a number dependence of the form factor amplitudes originates from the dynamical role of the ground state correlations and the gross number dependence of the occupation coefficients vv and uu, and that the number dependence of the form factor amplitudes provides .an explanation to the sign change of the interference observed in the middle of a major shell. In § 2, the transition amplitude for the A(p, t)B reaction is given in a second­ order perturbative form of the CCBA description. In this procedure, it is shown that the amplitude of the core-excitation model studied by Kozlowsky et aFl is